(x-12)(x-13)=0

Solution for (x-12)(x-13)=0 equation:

Simplifying
(x + -12)(x + -13) = 0

Reorder the terms:
(-12 + x)(x + -13) = 0

Reorder the terms:
(-12 + x)(-13 + x) = 0

Multiply (-12 + x) * (-13 + x)
(-12(-13 + x) + x(-13 + x)) = 0
((-13 * -12 + x * -12) + x(-13 + x)) = 0
((156 + -12x) + x(-13 + x)) = 0
(156 + -12x + (-13 * x + x * x)) = 0
(156 + -12x + (-13x + x2)) = 0

Combine like terms: -12x + -13x = -25x
(156 + -25x + x2) = 0

Solving
156 + -25x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(12 + -1x)(13 + -1x) = 0

Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {12, 13}